Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot

Matthew Hedden; Min Hoon Kim; Thomas E. Mark; Kyungbae Park

doi:10.1090/tran/7786

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arXiv · 1802.08620

Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot

Matthew Hedden·Min Hoon Kim·Thomas E. Mark·Kyungbae Park

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Abstract

We give two infinite families of examples of closed, orientable, irreducible 3-manifolds $M$ such that $b_1(M)=1$ and $\pi_1(M)$ has weight 1, but $M$ is not the result of Dehn surgery along a knot in the 3-sphere. This answers a question of Aschenbrenner, Friedl and Wilton, and provides the first examples of irreducible manifolds with $b_1=1$ that are known not to be surgery on a knot in the 3-sphere. One family consists of Seifert fibered 3-manifolds, while each member of the other family is not even homology cobordant to any Seifert fibered 3-manifold. None of our examples are homology cobordant to any manifold obtained by Dehn surgery along a knot in the 3-sphere.

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BibTeX RIS

Matthew Hedden, Min Hoon Kim, Thomas E. Mark, Kyungbae Park. 2018-02-23. Irreducible 3-manifolds that cannot be obtained by 0-surgery on a knot. https://doi.org/10.1090/tran/7786

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